scholarly journals Learning crystal field parameters using convolutional neural networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Noah F. Berthusen ◽  
Yuriy Sizyuk ◽  
Mathias Scheurer ◽  
Peter Orth
Keyword(s):  
Crystal Field ◽  
Ground State ◽  
Wavelet Transformation ◽  
Learning Algorithm ◽  
Tetragonal Symmetry ◽  
Specific Heat Data ◽  
Crystal Fields ◽  
Fitting Procedures ◽  
Crystal Field Parameters ◽  
Heat Data

We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion approximation and further processed using a standard wavelet transformation. We apply the method to crystal fields of cubic, hexagonal and tetragonal symmetry and for both integer and half-integer total angular momentum values JJ of the ground state multiplet. We evaluate its performance on both theoretically generated synthetic and previously published experimental data on CeAgSb_22, PrAgSb_22 and PrMg_22Cu_99, and find that it can reliably and accurately extract the CF parameters for all site symmetries and values of JJ considered. This demonstrates that CNNs provide an unbiased approach to extracting CF parameters that avoids tedious multi-parameter fitting procedures.

Investigations of the EPR g Factors for Er3+ in CaMoO4

2004 ◽  
Vol 59 (6) ◽  
pp. 341-345 ◽  
Author(s):  
Shao-Yi Wu ◽  
Hui-Ning Dong
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Crystal Field ◽  
Structural Data ◽  
Order Perturbation ◽  
Tetragonal Symmetry ◽  
Superposition Model ◽  
Paramagnetic Resonance ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic ◽  
G Factors

The electron paramagnetic resonance (EPR) g factors g‖ and g⊥ for Er3+ in CaMoO4 are theoretically investigated by using the perturbation formulas of the g factors for a 4f11 ion in tetragonal symmetry. In these formulas, the contributions to the g factors arising from the second-order perturbation terms and the admixture of various states are considered. The crystal-field parameters for the tetragonally distorted tetrahedra are determined by using the superposition model and the structural data of the impurity Er3+ on the host Ca2+ site in CaMoO4. The calculated g factors agree with the observed values. The validity of the results is discussed.

Theoretical Studies of the EPR Parameters of Nd3+ in LiYF4

2004 ◽  
Vol 59 (4-5) ◽  
pp. 235-238 ◽  
Author(s):  
Shao-Yi Wu ◽  
Hui-Ning Dong
Keyword(s):  
Electron Paramagnetic Resonance ◽  
Crystal Field ◽  
Structural Parameters ◽  
Tetragonal Symmetry ◽  
Theoretical Studies ◽  
Superposition Model ◽  
Paramagnetic Resonance ◽  
Epr Parameters ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic

The perturbation formulas of the electron paramagnetic resonance (EPR) parameters g∥, g⊥, A∥ and A⊥ for a 4f3(Nd3+) ion in tetragonal symmetry are established in this work. In these formulas, the contributions to the EPR parameters arising from the second-order perturbation terms and the admixtures of different states are included. Then the above formulas are applied to a tetragonal Nd3+ center in LiYF4, where the related crystal-field parameters are calculated from the superposition model and the local structural parameters of the Y3+ site occupied by the impurity Nd3+. The EPR parameters and the optical spectra within the 4I9/2 and 4I11/2 states obtained in this work agree reasonably with the observed values.

scholarly journals Theoretical Studies On The Gyromagnetic Factors For Nd3+ In Scheelites-Type ABO4 Compounds

2004 ◽  
Vol 59 (12) ◽  
pp. 947-951 ◽  
Author(s):  
Shao-Yi Wu ◽  
Hui-Ning Dong
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Tetragonal Symmetry ◽  
Theoretical Studies ◽  
Superposition Model ◽  
Crystal Field Parameters ◽  
Relationship Of ◽  
Geometrical Relationship ◽  
Theory And Experiment ◽  
G Factors

The gyromagnetic factors for Nd3+ in scheelite-type ABO4 compounds (A = Cd, Ca, Pb, Ba;B = Mo, W) are theoretically studied by the perturbation formulas of the anisotropic g factors g∥ and g⊥ for a 4f3 ion in tetragonal symmetry. In these formulas, the contributions to the g factorsdue to the second-order perturbation terms and the admixtures of various energy levels are takeninto account. The relevant crystal-field parameters are determined by the superposition model andthe local geometrical relationship of the A2+ sites occupied by the impurity Nd3+. The obtained gfactors agree reasonably with the observed values. The discrepancies between theory and experimentare discussed.

Further studies of the enhanced nuclear magnet HoVO 4 - I. The crystal field and the Zeeman spectrum

1988 ◽  
Vol 416 (1850) ◽  
pp. 63-73 ◽  
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Zeeman Effect ◽  
Tetragonal Symmetry ◽  
Novel Approach ◽  
Magnetic Resonance Frequency ◽  
Nuclear Magnetic Resonance Frequency ◽  
Crystal Field Parameters ◽  
Van Vleck ◽  
Good Agreement

A novel approach is adopted to fit the experimental results for the Van Vleck paramagnet HoVO 4 . Within the ground manifold 5 I 8 , J = 8, the five parameters for a crystal field of tetragonal symmetry are adjusted to give values in agreement with the optical spectrum for the lowest energy levels: the ground singlet, the first excited doublet at 21 cm -1 , and the (accidental) triplet at 47 cm -1 . Within experimental error (of order 1 cm -1 ), this agreement is not impaired by a small modification in which all the crystal field parameters are multiplied by a factor 1.0225. This factor is introduced to give the correct value of the enhanced nuclear magnetic resonance frequency for the stable isotope 165 Ho ( I = 7/2), known to 0.3% (Bleaney et al. Proc. R. Soc. Lond . A 362, 179 (1978)). The optical Zeeman effect, calculated therefrom, is in good agreement with that observed experimentally for the lowest levels in magnetic fields up to 15 T, directed along the [100], [110] and [001] axes (Battison et al. Phys. Lett . A 55, 173 (1975); J. Phys . C 10, 323 (1977)).

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

Ground configuration splitting in UCl5

1977 ◽  
Vol 55 (10) ◽  
pp. 937-942 ◽  
Author(s):  
A. F. Leung ◽  
Ying-Ming Poon
Keyword(s):  
Crystal Field ◽  
Energy Levels ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Coupling Constant ◽  
Point Charge Model ◽  
X Ray Crystallography ◽  
Charge Model ◽  
Crystal Field Parameters

The absorption spectra of UCl5 single crystal were observed in the region between 0.6 and 2.4 μm at room, 77, and 4.2 K temperatures. Five pure electronic transitions were assigned at 11 665, 9772, 8950, 6643, and 4300 cm−1. The energy levels associated with these transitions were identified as the splittings of the 5f1 ground configuration under the influence of the spin–orbit coupling and a crystal field of C2v symmetry. The number of crystal field parameters was reduced by assuming the point-charge model where the positions of the ions were determined by X-ray crystallography. Then, the crystal field parameters and the spin–orbit coupling constant were calculated to be [Formula: see text],[Formula: see text], [Formula: see text], and ξ = 1760 cm−1. The vibronic analysis showed that the 90, 200, and 320 cm−1 modes were similar to the T2u(v6), T1u(v4), and T1u(v3) of an UCl6− octahedron, respectively.

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

2021 ◽  
Vol 76 (4) ◽  
pp. 299-304
Author(s):  
Fu Chen ◽  
Jian-Rong Yang ◽  
Zi-Fa Zhou
Keyword(s):  
Crystal Field ◽  
Elongation Ratio ◽  
Paramagnetic Resonance ◽  
Local Structures ◽  
Epr Parameters ◽  
Structure Constants ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic ◽  
Theoretical Results ◽  
Good Agreement

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

Pseudocontact shifts in lanthanide complexes with variable crystal field parameters

2011 ◽  
Vol 255 (23-24) ◽  
pp. 2810-2820 ◽  
Author(s):  
Sebastiano Di Pietro ◽  
Samuele Lo Piano ◽  
Lorenzo Di Bari
Keyword(s):  
Crystal Field ◽  
Lanthanide Complexes ◽  
Pseudocontact Shifts ◽  
Crystal Field Parameters
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